# The regular black hole in four dimensional Born-Infeld gravity

## TL;DR

This paper demonstrates the existence of a regular black hole solution in four-dimensional Born-Infeld gravity, replacing the singularity with a cosmic string and ensuring geodesic completeness without matter or topology changes.

## Contribution

It introduces a novel regular black hole interior in Born-Infeld gravity, characterized by a new length scale and a non-singular core replacing the classical singularity.

## Key findings

- Replaces Schwarzschild singularity with a cosmic string.
- Ensures geodesic completeness of the black hole spacetime.
- Introduces a new length scale related to Born-Infeld parameter.

## Abstract

In the context of Born-Infeld gravity theories we report the existence of a regular black hole interior representing a spherically symmetric vacuum solution of the theory. It reduces to the Schwarzschild interior metric in the weak field region. In particular, there is a new length scale which is related to the Born-Infeld parameter. This endows the spacetime with an inner (i.e. well inside the event horizon) asymptotic region which is unattainable for observers. The central curvature singularity is replaced by an infinitely long cosmic string with constant curvature invariants related to the Born-Infeld constant. The presence of this limiting curvature spacetime renders the black hole timelike and null geodesically complete, free from the classical Schwarzschild singularity. The transition between the usual black hole interior and this maximum curvature space is achieved without introducing any kind of matter content nor topological changes.